Month: January 2013

Note: Sadly, I have noticed that the code of LaTex changes in WordPress. As an example, the text “\textdegree” use to provide the ˚ symbol but now provides ““. As such, please be patient and do not blame me for all editor faults! 🙂 It truly is an experiment in progress and I am dependent upon LaTex and WordPress consistency.

Conclusion: The molar flux of water is greater than sarin. As such, I assume the evaporation of water is greater than sarin. The latter is supported by a relative volatility (water:sarin) that is 12.6 at the specified conditions. Also, the boiling point of sarin is greater than water.

1991 Gulf War Illness

Before I continue, I would like the reader to know that more than 250,000 United States 1991 Gulf War veterans are suffering from 1991 Gulf War Illnesses. The illness can be psychologically and medically debilitating. For more information and to provide support, please please read the December 2012 scientific journal articles that connect chemical weapons to potential cause of illnesses[7;8]. Also, I wrote a post about differing hypotheses and 1991 Gulf War Illness[17].

Actual mathematical properties of a potential drop

Equation:

The base:

The base radius: 2.3 millimeters; The height: 1 millimeter

Drop volume: Double integration in polar coordinates

In polar coordinates

R is a unit disk in the xy plane and one reason I can use polar coordinates.

The moles of sarin evaporated per square centimeter per unit time may be expressed by[1]

Total molar concentration, c

The gas constant “R” will be calculated at standard temperature and pressure, “STP”

Conversion:

Sarin diffusivity in air at 10 deg Celsius and 1 atmosphere[16]

Assume the gas film

Mole fraction Sarin

From[13a]:

Sarin vapor pressure:

Conversion:

Assume no sarin in the air at a distance away from drop,

For a binary system

The sarin flux

Water

The moles of water evaporated per square centimeter per unit time may be expressed by[1]

Total molar concentration, c

As before, the gas constant “R” will be calculated at standard temperature and pressure, “STP”

Conversion:

Water diffusivity in air at 10 deg Celsius and 1 atmosphere[16]

Assume the gas film

Mole fraction of water

From[4]:

Water vapor pressure:

Constants A, B, C[Appendix A;4], T in kelvins, and pressure is in bar

Conversion:

From[2] and relative humidity of 71% (January weather in Iraq)[9]

Partial pressure of water in flowing stream

Relative humidity[2]:

At 283 K, previous equation gave:

For a binary system

Molar flux of water

Conversion:

Molar Flux: Sarin versus water comparison

Sarin:

Water:

Ratio:

Although the above is a simple evaluation based on “diffusion through a stagnant gas film”[1] and not the most rigorous, the ratio makes since because the ratio of vapor pressures at 10 deg Celsius, “relative volatility”[18], is

Per US Department of Energy[19]

“The evaporation of a liquid depends upon its vapor pressure — the higher the vapor pressure at a given temperature the faster the evaporation — other condition being equal.

The higher/lower the boiling point the less/more readily will a liquid evaporate.”[19]

Diffusivity of Water versus Sarin in Air at 10 Degrees Celsius (50 Degrees Fahrenheit) and 1 Atmosphere[see bottom of post]

1991 Gulf War veterans are suffering from 1991 Gulf War Illness[3;References]. Scientific research suggests the combination of experimental medication, pyridostigmine bromide as an example, over use of pesticides, chemical weapon-sarin as an example-destruction at plants and football sized bunkers, oil fires, etc as the potential cause[6-9].

Dr. Robert Haley, MD, UT SouthWestern Medical Center, and Intelligence Analyst James Tuite have reported how 1991 Gulf War veterans might have been contaminated with chemical weapons prior to the ground war, “Desert Storm”[9]. In fact, their work provides data proving that sophisticated equipment detected chemical weapons in Saudi Arabia prior to the ground war[9a]. It is also hypothesized that the “toxic cocktail” has caused autonomic dysfunction, nerve death, and brain death[9-14].

As a 1991 Gulf War veteran, I have been affected. I am also a chemical engineer with a degree in biological sciences. Like most educated, I have lost much of my knowledge in chemical engineering and biological sciences, but I can, if I find a good example, still “plug and chug” by using “tested and trusted” equations, which is advised anyhow. 🙂 Here, I compare the diffusivity of sarin vapor and water vapor in air by using Chapman and Enskog equation with Brokaw relations for polar gases correction. I have shown that the equation can be used when considering the diffusivity of polar in a non-polar matrix[19]. After performing the latter calculation, I noticed that reference [1] also suggests Brokaw relations to be used for diffusivity of one polar gas molecule in a non-polar matrix[1].

I will be comparing the diffusivity of polar sarin = A in non-polar air = B at 10C and 1 atmosphere. I chose 10C because I discovered data, possibly experimental, that stated that 90% volume of 1 mm sarin drop on a non-absorbable surface at 10C evaporated in 0.24 hours[17].

Equations

Chapman and Enskog Equation[1]. Reference [1] reports that this equation has a “Average absolute error” of 7.9% when used without Brokaw relations. The range is from 0% to 25%. The authors[1] did not provide an average for Browkaw relations but do provide specific absolute error values. When I averaged the Brokaw values[1], I obtained a 10.9% average absolute error with a range from 0% to 33%.

Chapman and Enskog Equation[1]

Neufield, et al. Equation

Polar Gases: Brokaw Relations

When is chosen as unity and “n” is expressed by the ideal-gas law, the Chapman-Enskog Equation

Brokaw Diffusivity: Water in Air at 10C and 1 Atmosphere

Molecular Weight

Water:

Air: 1 mole basis

Grams oxygen:

Grams nitrogen:

Air:

Need:

Note: I will only be calculating a delta value for water because air is non-polar[1;19].

Methyl mercaptan[3-6], “methanethiol”, is the byproduct of many natural processes. Flatulence is one example[7]. Because of its odor threshold, 1 ppb has been reported[4], methanethiol is also added to odorless natural gas, methane, and odorless propane for detection purposes. Apparently, it is used as a communication warning system in mining operations as well[4].

In this blog post, I will be comparing the diffusivity of the polar chemical methanethiol to the non-polar chemicals methane and propane in air. I have heard reports that the diffusivity of methanethiol is significantly greater than methane and propane. See bottom of post for diffusivities.Since reference[1] has tabular values for methane and propane in appendix B, I will use the tabular values and the Chapman-Enskog equation to calculate diffusivity values for methane and propane. For methanethiol, I will use Fuller, et al equation and tabular values for the atoms making up methanethiol,

Chapman-Enskog Equation. From reference[1], the average absolute error of this “theoretical equation” is 7.9%

If is chosen as unity and “n” expressed by ideal-gas law

For Non-polar gases: Methane and Propane

Methane in air at 25C and 1 atmosphere (atm)

Need

Neufield, et al.:

From appendix B[1]

Methane:

Air:

Diffusivity of Methane in Air:

Propane in air at 25C and 1 atmosphere (atm)

Need

Neufield, et al.:

From appendix B[1]

Propane:

Air:

Diffusivity of Propane in Air:

For polar molecule , will use Fuller, et al. equation. From reference[1], the absolute relative error of this equation is 5.4%. Authors report an average absolute error of about 4% when using

At a detection threshold of 1 part per billion (ppb) and the above diffusivities, one might detect methanethiol prior to experiencing propane. In truth, there is an equation that takes “mixture” into account but I do not know the percent mixture of each component[2].

Equation for mixture

is the mole fraction of component “n” in the gas mixture evaluated on a component-1-free basis

There are suggested correction factors for polar compounds. Since water is a polar compound, I will use these factors in a later comparison. I am doing a non-polar comparison because I was surprised with the closeness of the Hirschfelder equation previously when using non-polar factors.

Hirschfelder, Bird, and Spotz equation[2]

T = 298 K; P = 1 atm

Need . For comparative purposes, will use tabular values from [1].

Water:

Air:

Need to calculate

Neufeld, et al.:

The constants

A;B;C;D;E;F;G;H will be placed in the Neufeld, et. al. equation

First calculate

Back to Hirschfelder equation

Compared to experimental value from [2] at 25C and 1 atm

Diffusivity of water in air:

Chapman and Enskog equation

T = 298 K; P = 1 atm;

Compared to Hirschfelder equation and experimental value

Hirschfelder[2]:

Percent Difference:

Experimental:

Chapman[1]:

Percent Difference:

Polar Molecule Correction Comparison

Sadly, I have discovered that most empirical correlations lack sufficient data to estimate the diffusivity of many compounds. As an example, I, as a 1991 Gulf War veteran, desire to calculate the diffusivity of sarin in air. I have discovered that most empirical correlations do not take the phosphorus atom into consideration. Also, the Brokaw relationships for polar gases have correction equations that consider polar diffusing through polar.

In my analysis, I will first use the Brokaw method and only consider the polar molecule of water since air is non-polar. I will highlight the potential error of using this method by “error” when I use the correction equations. To be specific, will be calculated based on the new variable instead of a of two polar species. I hope to see if I can use the Brokaw method to calculate the diffusivity of sarin in air since the correction factors used in the Brokaw method include phosphorus and fluorine. I wish I could have found a phosphorus “diffusion volume increment”, , but I could not find one. I did find a fluorine[1], Nitrogen, Sulfur, Iodine, etc and might use either Nitrogen or Sulfur in the Fuller, et al. equation as an estimate when I calculate the diffusivity of sarin in air.

Since both equations gave approximately the same value during the non-polar comparison, I will use the Chapman-Enskog equation. Once again, the temperature and pressure are 25C and 1 atmosphere.

Chapman-Enskog equation[1]

T = 298 K; P = 1 atm

Brokaw Method

Neufield, et al. Relation:

Possible error: Since air is non-polar, I will only be using the delta of water, in the above equation.

Changed equation:

For Water (A)

Calculation by Le Bas method[1]

Percent Difference:

Note: ChemSpider provides a “Molar Volume” of for water. Although I assume the latter was calculated at normal boiling point, I am not certain. Still, the value is extremely close to the experimental value in reference [1], . For this reason, I will use the Chemspider value for water. Why? ChemSpider also provides a Molar Volume value for Sarin. If ChemSpider responds by email that the value was not calculated at boiling point, I will reconsider. Still, the percent difference of ChemSpider for water Molar Volume when compared to experimental[1] is:

ChemSpider Percent Difference:

Delta:

Need:

Water:

From [1]: Air:

Neufield, et al. Relation

Brokaw relation for polar molecules

Changed for water only:

Check Chapman and Enskog equation

T = 298 K; P = 1 atm;

Need:

From Brokaw relation

Chapman and Enskog equation for diffusivity of polar water in non-polar air

Non-polar versus polar comparisons

Using: and Brokaw relationships for polar corrections

Chapman and Enskog non-polar molecule[1]:

Chapman and Enskog with Brokaw relationships for polar molecules[1]:

Hirschfelder nonpolar[2]:

The experimental value[2]:

Note: All the ‘calculated” values are quite close. As such, I assume I can, when needed, use Chapman and Enskog and the Brokaw method to calculate the diffusivity of a polar molecule of sarin in non-polar air.